Abstract: Euclid is a European Space Agency (ESA) plan to start space galaxy survey in 2022．ESA will use two complementary cosmological probes to capture signatures of the expansion rate of the Universe and the growth of cosmic structures-galaxy clustering and cosmic shear, to study the dark energy model of interaction. Here we simulate Euclid galaxy survey data with nonlinear theoretical uncertainty error, and use Markov Chain Monte Carlo (MCMC) algorithm to constrain interacting dark energy model (wCDM) in complete parameter space with cosmic microwave background radiation (CMB), baryonic acoustic oscillation (BAO) and type Ia supernovae (SNe Ia)．To study restriction ability of Euclid on coupling constant (β), dark energy equation of state (w) and other parameters of different interaction dark energy models, we compared four interaction dark energy models with CMB + BAO + SNe and Euclid + CMB + BAO + SNe．Euclid + CMB + BAO + SNe were found to give more stringent constraints on interacting dark energy models except \rmQ_\rmde \propto 3\beta H\rm\rho _\rmde\rm\nu _\rmde．With CMB+BAO+SNe, deviations of β from 0 were found to be >1.2σ for all four models．With Euclid+CMB+BAO+SNe, deviations of β from 0 were >1σ for models of Q_\rmde \propto 3\beta H\rm\rho _\rmc\rm\nu _\rmc, Q_\rmde \propto 3\beta H\rm\rho _\rmc\rm\nu _\rmde, Q_\rmde \propto 3\beta H\rm\rho _\rmde\rm\nu _\rmc, but were >1.9σ for Q_\rmde \propto 3\beta H\rm\rho _\rmde\rm\nu _\rmc．Euclid is a potential survey experiment, combined with CMB, SNe, Hubble parameter data (OHD) and other cosmological probes．Euclid will help to further understand properties of dark energy and dark matter．